Problem: A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: $P(x)=-3(x-5)^2+12$ What sock price should the company set to earn a maximum profit?
Explanation: The company's profit is modeled by a quadratic function, whose graph is a parabola. The maximum profit is reached at the vertex. So in order to find when that happens, we need to find the vertex's $x$ -coordinate. The function $P(x)$ is given in vertex form. The vertex of $-3(x-{5})^2{+12}$ is at $({5},{12})$. In conclusion, the company will earn a maximum profit when the socks are priced at $5$ dollars.